Large Language Models~(LLMs) struggle with providing current information due to the outdated pre-training data. Existing methods for updating LLMs, such as knowledge editing and continual fine-tuning, have significant drawbacks in generalizability of new information and the requirements on structured updating corpus. We identify the core challenge behind these drawbacks: the LM-logical discrepancy featuring the difference between language modeling probabilities and logical probabilities. To evaluate and address the core challenge, we propose a new task formulation of the information updating task that only requires the provision of an unstructured updating corpus and evaluates the performance of information updating on the generalizability to question-answer pairs pertaining to the updating information. We further propose a novel and effective pipeline approach for the task, highlighting a self-prompting-based question-answer generation process and a associative distillation methods to bridge the LM-logical discrepancy. We develop two datasets for evaluation, one sourced from news articles published in March and April 2023, and the other from the Natural Questions benchmark. Experimental results demonstrate the superiority of our approach, significantly increasing the factual consistency score (on a scale from 0 to 1) by up to 0.16. Furthermore, our method effectively mitigates forgetting utilizing a compact replay buffer with only 2.3% of the training tokens.
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